## Third Threshold Analysis

Some physicians may not want to spend the time extracting and estimating cost data, or they may harbor great suspicions against such iffy estimates. The physicians may feel that the clinical success rates of PUD and NUD associated with various treatment modalities have been well established by

 p (90%) ABX + 10% complication \$252
 P (70%) PPI + 30% complication \$1,506

FIGURE 2-4. Threshold analysis of ulcer management with antibiotics (ABX) versus proton pump inhibitors (PPI). NUD = nonulcer dyspepsia; p = probability of PUD; PUD = peptic ulcer disease.

FIGURE 2-4. Threshold analysis of ulcer management with antibiotics (ABX) versus proton pump inhibitors (PPI). NUD = nonulcer dyspepsia; p = probability of PUD; PUD = peptic ulcer disease.

many controlled clinical trials, but that the cost data are far less well substantiated. In essence, they would want to restrict their analysis to medical issues, such as the success rates of various therapies shown by the decision tree of Figure 2-5. The success rates from the previous decision tree now change to become the new outcomes of the revised tree. The same type of reasoning and calculation that was used in the first threshold analysis can be used here to extract the threshold value for p. For the upper ABX and the lower PPI branch to be equivalent, the following equation must apply:

The letters A through D are used to label the outcomes of the right column of boxes. Again, this equation can be ple 2 x 2 threshold analysis, a medical problem needs to be shaped into a relatively rigid form. The initial decision against or in favor of a medical action is followed by a set of probabilities (p versus 1 - p), which govern the occurrence of medical events. The probabilities should be independent of the action taken and, therefore, identical for both decisions, in the present scenario of ABX versus PPI. Each of the final outcomes is determined by the interaction between the action taken (decision made) and the probable medical event. In spite of its striking simplicity, this framework is able to capture and faithfully analyze a large variety of heterogeneous and often perplexing medical problems.

The letters A through D are used to label the outcomes of the right column of boxes. Again, this equation can be

solved algebraically for p to yield the following formula:

P

PUD

A

The formula applies similarly to all types of threshold analysis. Substituting the actual success rates from Figure 2-5 into the formula yields the following outcome:

NUD

1 - P

B

If the probability of peptic ulcer exceeds .33, it would be worthwhile to subject the patient to an empirical trial of antibiotics before committing him to any long-term therapy with PPI. This last example serves to illustrate that threshold analysis is not necessarily dependent on cost data and that, in principle, any outcome parameter can be used to calculate a threshold probability. To be phrased as a sim-

 PUD C 70%
 NUD 1 - P D 50%

FIGURE 2-5. Threshold analysis of ulcer management with antibiotics (ABX) versus proton pump inhibitors (PPIs). NUD = nonulcer dyspepsia; p = probability of PUD; PUD = peptic ulcer disease. The letters A through D are used to label the outcomes of the right column of boxes.

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